Laser Powder Bed Fusion (LPBF) is a widely adopted metal additive manufacturing technology that enables the fabrication of intricate metal components, yet it faces challenges arising from intrinsic residual stress and distortion development. High-fidelity thermomechanical simulations offer essential insights for predicting and mitigating these effects. The reliability of such simulations depends on various factors, but critically on the material input data, primarily the constitutive model which should accurately represent the material's deformation behaviour under the complex loading conditions expected during LPBF. The present study integrates an advanced elastic-viscoplastic constitutive model into the LPBF thermomechanical simulation, capable of capturing the cyclic response of LPBF Hastelloy X across a broad range of temperatures and strain rates, and accounting for both isotropic and kinematic hardening. Simulation outcomes are validated against in-situ temperature and distortion measurements obtained during an LPBF experiment for Hastelloy X. Acknowledging the extensive effort required to develop such an advanced constitutive model, this study also calibrates three alternative models of simpler formulation to assess the impact of model selection on simulation outcomes and computational cost. The four investigated models span from rate-dependent elastic-viscoplastic to rate-independent elastic-plastic formulations, each with different capabilities for representing the alloy's cyclic hardening response. The results provide valuable insights into trade-offs between simulation accuracy, constitutive model development effort, and computational efficiency in LPBF thermomechanical simulations.